Problem: Vanessa is 4 times as old as William and is also 21 years older than William. How old is William?
Solution: We can use the given information to write down two equations that describe the ages of Vanessa and William. Let Vanessa's current age be $v$ and William's current age be $w$ $v = 4w$ $v = w + 21$ Now we have two independent equations, and we can solve for our two unknowns. Since we are looking for $w$ , and both of our equations have $v$ alone on one side, this is a convenient time to use elimination. Subtracting the second equation from the first equation, we get: $0 =$ $4w$ $-$ $ (w + 21)$ which combines the information about $w$ from both of our original equations. Solving for $w$ , we get: $3 w = 21$ $w = 7$.